Solving Two-Dimensional Helmholtz and Poisson Equations Using Double Laplace Transform Method

Objectives: To explore the efficacy of the double Laplace transform technique in solving 2D Helmholtz and Poisson equations. Methods: The double Laplace transform clearly converts the 2D Helmholtz and Poisson equations into an algebraic calculation in the Laplace domain that can be solved easily. Findings: The double Laplace transform method offers exact solutions to the Helmholtz and Poisson equations by resolving a series of specific and understandable examples. Novelty: This research highlights the potential of double Laplace transform methods as a competent and flexible instrument for resolving 2D Helmholtz and Poisson equations. Mathematics Subject Classifications: 35R09, 35R11, 44A10, 44A30. Keywords: 2D Helmholtz Equation; Poisson Equation; Double Laplace Transform; Inverse Double Laplace Transform; Exact Solution